To convert a temperature from Celsius ([tex]${}^{\circ}C$[/tex]) to Fahrenheit ([tex]${}^{\circ}F$[/tex]), we use the following formula:
[tex]\[ F = C \times \frac{9}{5} + 32 \][/tex]
In this problem, we need to convert [tex]$-10^{\circ}C$[/tex] to Fahrenheit. We can proceed step-by-step:
1. Identify the temperature in Celsius: The given temperature is [tex]$-10^{\circ}C$[/tex].
2. Use the conversion formula: Plug in the Celsius value into the formula:
[tex]\[
F = (-10) \times \frac{9}{5} + 32
\][/tex]
3. Perform the multiplication:
[tex]\[
-10 \times \frac{9}{5} = -10 \times 1.8 = -18
\][/tex]
4. Add 32 to the result:
[tex]\[
-18 + 32 = 14
\][/tex]
Therefore, [tex]$-10^{\circ}C$[/tex] converts to [tex]$14^{\circ}F$[/tex].
So, on the label for the high temperature alarm, you should write:
[tex]\[ \boxed{14^{\circ}F} \][/tex]
